1. Field of the Invention
The present invention relates to an evaluating method for image formation performance of optical systems such as a projection optical system and an observation optical system used in photolithography, a coat designing method according to the evaluation, an optical system designing method according to the evaluation, an optical system, an optical system manufacturing method, a design program, a computer readable storage medium, a projection exposure apparatus, and a projection exposure method.
In addition, the present invention relates to a projection optical system, a manufacturing method thereof, and an exposure apparatus having the projection optical system, in particular, to a projection optical system suitable for an exposure apparatus used when microdevices such as a semiconductor device and a liquid crystal display device are manufactured by a photolithography processing.
2. Description of the Related Art
When a fine pattern of an electronic device (a microdevice) such as a semiconductor integrated circuit or a liquid crystal display is formed, in a known photolithography method, a pattern to be formed is proportionally enlarged around four to five times and drawn on a photo mask (also called a reticle). The pattern on the photo mask is reduced, exposed, and transferred onto a photosensitive substrate (target exposure substrate) such as a wafer using a projection exposure apparatus.
when an optical system such as a projection optical system used in the photolithography is designed, since the number of combinations of surface shapes, surface intervals, clear apertures, reflectivities, refractivities, tolerances, and so forth of lenses, mirrors, and so forth that compose the optical system is huge. Thus, a design solution that satisfies a request spec cannot be definitely obtained.
Thus, to obtain final data, image formation performance of the optical system is evaluated according to basic data by numeric calculations for tracing light rays and the like, and correction of the basic data is repetitively done until the image formation performance falls within the target range (hereinafter, a design for surface shapes, surface intervals, clear apertures, reflectivities, refractivities, tolerances, and so forth of optical elements that compose an optical system is referred to as “optical design”).
Note that calculations necessary for the optical design are automatically performed by a computer because increases in the number of optical devices complex the calculations exponentially.
Generally, coats specific to individual optical elements are formed on the surfaces thereof so as to prevent reflection, restrict transmission light, or increase reflection. The coats have influences on the image formation performance of the optical system, and the influences vary depending on the structures of the coats (for example, the number of layers, the thickness of each layer, the material of each layer, the absorption coefficient of each layer, and so forth). The influences also vary depending on what type of coats are formed on what surfaces of what optical elements.
In particular, the request spec for a projection optical system used in the photolithography is very high, and a large number of optical elements constitute the projection optical system. Therefore, the influence of coats formed on the optical elements is not ignorable. In addition, a reflection type projection optical system and a reflection-refraction type projection optical system have reflection surfaces on which a predetermined function is to be provided. Thus, coats formed on the reflection surfaces need to be multi-layered. Accordingly, the coats largely influence the image formation performance.
Thus, when a projection optical system is designed, in addition to the forgoing optical design, “coat design” and “coat allocation” are performed.
In the coat design, various types of coat data as design solutions such as the number of layers of coats, the thickness of each layer, the material of each layer, and so forth that satisfy a request for reflectivity characteristic (transmittance characteristic) are obtained.
In the coat allocation, with numeric calculations such as ray-tracing according to various coat data and pre-obtained design data of optical elements (final data and basic data), while image formation performance of the projection optical system is being evaluated, to obtain good image formation performance, it is determined that what type of coat data is allocated to what surface.
When the conventional coat allocation is evaluated, a pupil transmittance T0 of a light ray that passes through the center of an exit pupil surface and transmittances T1, T2, T3, . . . of several ten light rays that pass through an edge portion of the exit pupil surface are obtained from a light beam that enters the center of an image through the projection optical system. The degree of deviation of the obtained pupil transmittances T1, for example the difference Δ(=Tmax−Tmin) between the maximum value Tmax and the minimum value Tmin is referred to as evaluation index. The smaller the evaluation index Δ is, the better image formation performance it represents.
In the photolithography, to satisfy a request for a fine structure of semiconductor integrated circuits, the exposure light wavelengths are being shifted toward the short wave side.
At present, the main stream of the exposure light wavelengths is 248 nm of a KrF excimer laser. In addition, an ArF excimer laser that has a shorter wavelength of 193 nm is being entered into the practical stage.
Moreover, projection exposure apparatuses that use light sources of a F2 laser having a wavelength of 157 nm, a Kr2 laser having a wavelength of 146 nm, an Ar2 laser having a wave length of 126 nm, and so forth that supply light of a wavelength band that is so-called vacuum ultraviolet region have been proposed.
Furthermore, when the numerical aperture (NA) of a projection optical system becomes large, a high resolution can be accomplished. Thus, in addition to efforts for shortening the exposure light wavelengths, projection optical systems having larger numerical apertures have been developed.
Materials (lens materials) that have good transmittances and uniformity to ultraviolet exposure light having such a short wavelength are restricted.
In a projection optical system that uses an ArF excimer laser as a light source, synthesized silica as a lens material can be used. However, since the chromatic aberration cannot be sufficiently compensated with one kind of lens material, calcium fluoride crystal (fluorite) is used in some lenses.
On the other hand, in a projection optical system that uses an F2 laser as a light source, a lens material that can be used is substantially restricted to calcium fluoride crystal (fluorite).
However, the higher the resolution currently required for the photolithography, the higher the request spec for a projection optical system PL. Thus, it becomes necessary to properly suppress the influence of coats on the image formation performance.
To do that, in addition to the coat allocation according to the evaluated result using the forgoing evaluation index Δ, the coat design and optical design may be performed. In addition, an illumination optical system used in the photolithography may be designed.
However, in any manner, unless the influence of the coats accurately reflects the evaluation, the influence cannot be more properly suppressed.